Effect of buoyancy on the motion of long bubbles in horizontal tubes

As a confined long bubble translates along a horizontal liquid-filled tube, a thin film of liquid is formed on the tube wall. For negligible inertial and buoyancy effects, respectively, small Reynolds (Re) and Bond (Bo) numbers, the thickness of the liquid film depends only on the flow capillary number (Ca). However, buoyancy effects are no longer negligible as the diameter of the tube reaches millimeter length scales, which corresponds to finite values of Bo. We perform experiments and theoretical analysis for a long bubble in a horizontal tube to investigate the effect of Bond number (0.05 < Bo < 0.5) on the thickness of the liquid film and the bubble orientation at different capillary numbers 10(-3) < Ca < 10-1. We investigate several features of the lubricating film around the bubble. (i) Due to the gravitational effects, the film deposited on the upper wall of the channel is thinner than the film at the bottom wall. We extend the available theory for the film thickness at the front of the bubble in a two-dimensional geometry at low capillary numbers Ca < 10(-3) and finite Bo to account for the effect of larger Ca. The resulting model shows very good agreement with the present experimental measurements. (ii) Due to the asymmetry in the liquid film thickness and the consequent drainage of the liquid from the top to the bottom of the tube, the bubble is inclined relative to the channel centerline and our side-view visualizations allow direct quantification of the inclination angle, which increases with both Bo and Ca. While the inclination angle at the top is smaller than that at the bottom of the tube, the average of these two values follows the predictions of a mass balance analysis in the central region of the bubble. (iii) The inclination of the bubble causes the thickness of the thin film at the back of the bubble to depend on the length of the bubble, whereas the thickness at the front of the bubble does not depend on the bubble length.